Simplify the following expression: $ p = \dfrac{2n}{8n - 9} - \dfrac{10}{3} $
Answer: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{3}{3}$ $ \dfrac{2n}{8n - 9} \times \dfrac{3}{3} = \dfrac{6n}{24n - 27} $ Multiply the second expression by $\dfrac{8n - 9}{8n - 9}$ $ \dfrac{10}{3} \times \dfrac{8n - 9}{8n - 9} = \dfrac{80n - 90}{24n - 27} $ Therefore $ p = \dfrac{6n}{24n - 27} - \dfrac{80n - 90}{24n - 27} $ Now the expressions have the same denominator we can simply subtract the numerators: $p = \dfrac{6n - (80n - 90) }{24n - 27} $ Distribute the negative sign: $p = \dfrac{6n - 80n + 90}{24n - 27}$ $p = \dfrac{-74n + 90}{24n - 27}$